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SUMMARY:Hard-core configurations on Z^2 and other lattices - Izabella Stuh
 l (Penn State)
DTSTART:20190611T130000Z
DTEND:20190611T140000Z
UID:TALK125680@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The hard-core model attracted interest at an early stage of th
 e progress in the rigorous Statistical Mechanics\; its popularity increase
 d after recent successes in studying dense-packing configurations of hard 
 spheres in R^d\, for d = 2\,3\,8\,24 and in view of new applications\, in 
 particular in Computer Science and Biology. A lattice version of the same 
 problem emerges when the sphere centers are positioned at sites of a given
  lattice (or a graph). We focus on two problems: (i) specification of peri
 odic ground states (PGSs)\, i.e.\, configurations of the maximum density w
 hich cannot be ‘improved’ by a local change\, and (ii) identification 
 of the dominant GSs generating extreme Gibbs/DLR measures for large values
  of fugacity by means of the Pirogov-Sinai theory. This presentation will 
 be focused mainly (but not exclusively) on the case of a unit square latti
 ce Z2. We plan to touch upon a number of arising topics\, including slidin
 g\, tesselating\, counting PGSs and dominant PGSs and the Peierls conditio
 n.\nThis is a joint work with A. Mazel and Y. Suhov
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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